Visualization of complex functions by animation

This is a collection of flash animations for
visualizing maps of one complex variable. Each animation shows the image
of a domain in the complex plane as it morphed by a given function.
In mathematical terms we display the image of the domain under
a homotopy of maps ranging from the identity
to the given function, so the first frame of the animation shows the domain
and the last frame shows its image under the function. The domain is colored
with a pattern to make it easier to follow the homotopy.